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The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number

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PIASECKI K., SIWEK J.
Operations Research and Decisions
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2018
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vol. 28
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issue 1
57-74
EN
A multi-asset portfolio in the case of its present value estimated by a discrete trapezoidal fuzzy number has been assessed. The benefits of owning a security have been evaluated according to an expected fuzzy discount factor. The ambiguity risk has been assessed by an energy measure and indistinctness risk has been evaluated by Kosko’s entropy measure. The relationship between the expected fuzzy discount factor for a portfolio and the expected fuzzy discount factors for its components has been derived. An analogous relationship between the values of the energy measure has been presented. The model has been illustrated by means of a profound numerical case study.
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Modifications of order scales for assessing debtors

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WÓJCICKA-WÓJTOWICZ A., PIASECKI K.
Operations Research and Decisions
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2022
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vol. 32
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issue 3
142-151
XX
In previous research, the Extended Order Scale (EOS) dedicated to risk assessment was analysed. It was characterised by a Numerical Order Scale (NOS) evaluated by trapezoidal oriented fuzzy numbers (TrOFNs). However, the research showed that EOS with two-stage orientation phases, was too complicated. Therefore, the main aim of our paper is to simplify a Complete Order Scale (COS) to a zero- or one-stage order scale and a hybrid approach. For this purpose, a way to calculate the scoring function is presented. The results show that changes in the COS structure influence the values of a scoring function. Replacing just one linguistic indicator gives different results. Another finding of the research is the method’s flexibility that allows an expert to individually choose the most suitable COS. The research proves that the boundary between various linguistic labels cannot be precisely defined. However, knowledge of a formal COS structure allows it to be transformed into a less complex one.
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The present value of a portfolio of assets with present values determined by trapezoidal ordered fuzzy numbers

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ŁYCZKOWSKA-HANĆKOWIAK A., PIASECKI K.
Operations Research and Decisions
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2018
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vol. 28
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issue 2
41-56
EN
We consider the obvious thesis that the present value of a portfolio is equal to the sum of the present values of its components. The main goal of this paper is the implementation of this thesis in the case when present values are determined by trapezoidal ordered fuzzy numbers. We apply the revised sum of ordered fuzzy numbers. The associativity of such a revised sum is investigated here. In addition, we show that the multiple revised sum of a finite sequence of trapezoidal ordered fuzzy numbers depends on the ordering of its summands. Without any obstacles, the results obtained can be generalized to the case of any ordered fuzzy numbers.
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